Physical Quantities and Measurement Techniques

Measuring Tools

  1. Ruler: Measures length. Read markings directly.
    • Limitations: accuracy depends on tick spacing.
  2. Measuring Cylinder: Measures volume of liquids. Read meniscus at eye level to ensure accuracy.
  3. Clock: Measures duration of events. Digital timer used for short intervals to minimize reaction error.
  4. Pendulum Period:
    • Time for one complete oscillation. Measure multiple periods ($T_{total}$) and divide by count ($n$) to reduce timing error.
    • Formula: $$T = \frac{T_{total}}{n}$$

Scalars vs Vectors

  • Scalars: Quantities with magnitude only.
    • Examples: distance, speed, time, mass, energy, temperature.
  • Vectors: Quantities with magnitude and direction.
    • Examples: force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.

1.1.3 Resultant of Two Vectors

  • Two Vectors at Right Angles: Use Pythagoras theorem for magnitude.
    • Formula: $R = \sqrt{A^2 + B^2}$
  • Resultant Direction: Calculated using the inverse tangent function.
    • Formula: $\theta = \tan^{-1}\left(\frac{A}{B}\right)$ Image description: Two vectors forming a right-angled triangle with the resultant vector as the hypotenuse

Motion

Definitions

Speed: Distance divided by time. Scalar quantity.
Formula: $$\text{s} = \frac{\text{d}}{\text{t}}$$

Velocity: Speed in a given direction. Vector quantity.

Average Speed: Total distance divided by total time.
Formula: $$v_{avg} = \frac{d_{total}}{t_{total}}$$

Distance-Time Graphs

Axis: Time (horizontal), Distance (vertical).

Interpretation:

  • At rest: Horizontal line (gradient = 0).
  • Constant speed: Straight line with steady positive gradient.
  • Accelerating: Curve getting steeper (positive gradient increases).
  • Decelerating: Curve getting less steep (positive gradient decreases).

Speed from Graph: Gradient (rise over run). Image description: Distance-time graph showing straight line and curved sections representing acceleration

Speed-Time Graphs

Axis: Time (horizontal), Speed (vertical).

Interpretation:

  • At rest: Line on time axis (speed = 0).
  • Constant speed: Horizontal line.
  • Constant acceleration: Straight line starting from origin (speed increases linearly).
  • Changing acceleration: Curved line.
  • Distance from Graph: Area under the curve.
    • Rectangular area: Constant speed.
    • Triangular area: Constant acceleration.
  • Deceleration: Negative acceleration. Gradient is negative.

Image description: Speed-time graph with positive gradient (acceleration) and negative gradient (deceleration)

Acceleration and Free Fall

Acceleration: Change in velocity divided by time.

  • Formula: $a = \frac{\Delta v}{t}$

Free Fall: Acceleration due to gravity.

  • Formula: $g \approx 9.8 \text{ m/s}^2$ near Earth’s surface.

Motion in Uniform Gravitational Field:

  • Without Resistance: Constant acceleration downward ($9.8 \text{ m/s}^2$).
  • With Air/Liquid Resistance: Object reaches terminal velocity (constant speed when downward force = upward resistance). Speed no longer increases.